1. Field of the Invention
The present invention relates to an apparatus for optically generating chaotic random numbers satisfying a chaotic dynamical system that is expressed X(n+1)=F(X(n)), using an optical circuit.
2. Description of the Prior Art
Methods for producing random-number sequences are roughly divided into two. One of them uses a random number generator program memorized in a digital computer. The program corresponds to an existing pseudo-random-number generating program that includes (1) congruent random numbers produced by a modulus of congruence that is a random-number producing algorithm required in the Monte Carlo method applied to various fields, such as device modeling, finance derivative calculation and the like, (2) M sequences and (3) Gold codes that are random-number sequences produced by a shift register required in spread spectrum communication systems. The numbers, sequences and codes have heretofore been used widely.
The other method generates so-called physical random numbers from noise unavoidably inherent in a physically fabricated electronic circuit or electronic device. Since a micro-mechanism for generating such random number is unclear or complicated, this method lacks in repeatability of producing same random-number sequences under the same initial conditions and is improper for engineering random-number applications.
There is another method for generating so-called laser chaos as a chaotic random-number signal using an optical circuit with a time-lag feedback loop laser. However, since the equation expressing a signal is a non-linear, partial differential equation difficult to analyze, it is difficult to qualitatively predict the features of the random numbers. For this reason, an optical communication system on the order of terabit/sec having a random-noise generating portion has been neither put into practice nor commercialized. The incorporation of laser chaos into such a random-noise generating portion is in an experimental stage, and the integration of such random noise generating portions is difficult to realize due to the lack of the integration optic technology toward laser chaos.
The speed of transmitting a signal of random numbers in a digital computer or physical random numbers in an electronic circuit has its own limits due to the fact that electronic devices put into practical use are operated at a frequency of about 600 MHz. Therefore, the physical random-number generating method based on conventional electronic circuits or devices cannot be used for data transmission at a high-speed bit rate, such as terabit/sec for transmitting an animated cartoon etc. Further, the method for producing signals using optical laser chaos does not have good respectability because of the complexity of a system using the method and has a difficulty in generating random numbers easy to control, unlike the M sequences produced by a shift register, due to the difficulty of an engineering design requiring high precision.
In the conventional Monte Carlo computation, the calculation speed is determined by a stable operation speed of a semiconductor device. The pseudo-random-number generating program used in the Monte Carlo method clearly constitutes the performance of a digital computer and eventually the digital computer per se. For this reason, the high-speed calculation in the Monte Carlo method subjected to various applications has its own limits due to the electronic device operating limit (that is theoretically about 750 GHz, but practically about 600 MHz shown above, "Wrestling with Switching Optical Technique at Terabit/sec," Nikkei Electronics, p. 109, Jun. 29, 1998).
The present invention has been proposed to solve the problems of the limit of the random-number producing speed and the control thereof. The principal object of the present invention is to provide an apparatus for optically generating chaotic random numbers, that is high in repeatability of producing physical random numbers and easy to control, using the high-speed property of light and the deterministic properties and random numbers in a chaotic dynamical system.
Another object of the present invention is to provide an apparatus for optically generating chaotic random numbers, that enables data transmission at terabit/sec.